I have prepared an excel sheet to calculate yield moment and curvature for a hollow circular section. In which Depth of Neutral Axis is fixed using "GOAK SEEK" function. Axial Force is input of the excel program.
The steps are: divide the section in number of small parts, calculate strain at each layer of concrete and steel by fixing the yield strain in bottom most steel level, calculate stress, forces and moment.
The problem is when I fix the yield strain in bottom fiber top compression stress exceeds the ultimate limit. What to do here?
I am attaching the excel here. Please check formula in cell W21, what I have done is if strain the the layer exceeds ultimate strain of concrete I have taken the value of concrete for that layer as 0 and hence stress, force for those layers becomes 0. Is this correct? or I have to take ultimate strain of concrete for those layers.
Concrete sections have two limit state criteria.
1-tension yielding of steel
2- compression failure of concrete
Thus your excel sheet should contain both of these two. If any of the two criteria
occurs, the section is failed and limit state is reached.
Dear Megha Bhatt
firstly, I agree with Dr Ali Jalaeefar about failure conditions in concrete sections,.
secondly, when strain of each layer reach to ultimate strain of concrete in compression zone due to concrete nature, when strain of each layer reach to ultimate strain of concrete in compression zone due to concrete nature, it crack and this cracking will distribute in height of the section rapidly. after few moments concrete section will collapse. therefore in my point of view, whenever strain of each layer reach to ultimate strain of concrete, strain of the layer must be ultimate strain and stress of the layer must be zero.
The 2 abovementioned ultimate conditions of r/c sections together with the material σ-ε relationships are the solution of your problem.
In general, ultimate conditions in reinforced concrete are shown as:
a) in monotonic loading, with a characteristic drop (about 20%) of the section moment resistance after the peak.
b) in cyclic loading, with an abrupt degradation of stiffness and strength associated with a drop of about 20% of the maximum ever moment resistance. Therefore, the ultimate material strain is recorded at 80% of the maximum moment resistance.
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